When I boot my computer, the purple Ubuntu splash appears (without the orange dots) for a split second, and then the screen turns black. I was able to get the Xorg.0.log from the command line. I think this happened after installing the proprietary drivers for my Radeon HD 6770.

You will be prompted to agree to a license agreement. Do not build the distribution-specific driver package when given the option. Go with the "Standard" or non-"Expert" install type. Enter through all the other options. Wait until you are allowed to return to the prompt and press Ctrl+Alt+Delete to reboot.